Gradient estimates for singular elliptic measure data problems with double phase
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914577846894592 |
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| author | Song, Kyeong Youn, Yeonghun Zatorska-Goldstein, Anna |
| author_facet | Song, Kyeong Youn, Yeonghun Zatorska-Goldstein, Anna |
| contents | We consider elliptic measure data problems of the type \[ -\mathrm{div}\,(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du) = μ\] in a bounded domain in $\mathbb{R}^n$, where $p<q$ and $a(\cdot) \ge 0$. We prove local Calderón--Zygmund estimates in the singular case $2-1/n < p < 2$, under natural assumptions on $p$, $q$ and $a(\cdot)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18235 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gradient estimates for singular elliptic measure data problems with double phase Song, Kyeong Youn, Yeonghun Zatorska-Goldstein, Anna Analysis of PDEs 35B65, 35J75, 35R05, 35R06 We consider elliptic measure data problems of the type \[ -\mathrm{div}\,(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du) = μ\] in a bounded domain in $\mathbb{R}^n$, where $p<q$ and $a(\cdot) \ge 0$. We prove local Calderón--Zygmund estimates in the singular case $2-1/n < p < 2$, under natural assumptions on $p$, $q$ and $a(\cdot)$. |
| title | Gradient estimates for singular elliptic measure data problems with double phase |
| topic | Analysis of PDEs 35B65, 35J75, 35R05, 35R06 |
| url | https://arxiv.org/abs/2605.18235 |